# Lat18

### Logic and Automata Theory

**Lecturer**: Radu_Iosif

**Objectives**: Many major hardware (Intel, IBM) and software (Microsoft) companies are now using the technique of Model Checking in practice. Examples of its use include the verification of VLSI circuits, communication protocols, software device drivers, real-time embedded systems, and security algorithms. The works of A. Pnueli, E. Clarke, E.A Emerson and J. Sifakis on algorithmic verification of systems using the Model Checking has been awarded the 1996 and 2007 Turing awards. The basis of this work is the relation of logic with automata theory, which was introduced by the seminal works of Buechi (1960) and Rabin (1969). This course is intended to introduce the student to these techniques, focusing on decision methods for classical non-interpreted logics and integer arithmetic theories.

**Syllabus**:

- Classical first- and second-order logic, finite word and tree automata, closure properties and language emptiness.
- Relationship between Weak Monadic Second-Order Logic and finite automata.
- Infinite automata on words (Buechi, Mueller) and on trees (Rabin) automata, and their relationship with Monadic Second-Order Logic.
- Game theory. Proof of Rabin's Complementation Theorem. Application of game theory to logic.

**Prerequisites**: basic notions of boolean logic

**Level**: PhD and Master 2

**Schedule**: Mondays between 10h00 and 13h00

- Oct 08: Introduction, First and Second Order Logics
- Oct 15: Automata on Finite Words
- Oct 22: Automata on Infinite Words
- Oct 29: McNaughton's Theorem, Model Checking 1, Model Checking 2
- Nov 05: Automata on Finite Trees
- Nov 12: Automata on Infinite Trees
- Dec 3: Game Theory Motivation, Terminology, Reachability and Buchi games
- Dec 10: Staiger-Wagner and Weak Parity Games Parity games Games and Tree Automata

**Resources**:

- Automata on Infinite Trees lecture by Wolfgang Thomas
- Textbook proof of McNaughton's Theorem
- GOAL - Graphical Tool for Omega-Automata and Logics
- Game Examples for GOAL
- M. Vardi and P. Wolper. Reasoning about Infinite Computations
- M. Vardi. From Philosophical to Industrial Logics slides
- Java Concurrency Analysis Tool

**Location**: IMAG building, Room: 206

**Register**:

- send email to Radu.Iosif@univ-grenoble-alpes.fr indicating your name and year of Phd/Master program
- for PhD students, indicate also your host laboratory and name of your PhD advisor